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Calculus Questions & Answers

Q:
A certain tranquilizer decays exponentially in the bloodstrean and has a half-life of 22 hours. How long with it take for the drug to decuy to \( 82 \% \) of the original dose? a) step 1 : Find K (Round to four decinal pleces) b) step \( 2: \) Use \( k \) to determine how longlinhours) it will take for the devg to decay to \( 82 \% \) of the original dose. (Round to one decinalplace)
Q:
Question Approximate the \( x \)-value of the local minimum value of the function given below. Use Newton's method with the specified initial approximation \( x_{0} \) to find \( x_{2} \). Round your answer to the nearest thousandth. \[ f(x)=\frac{5}{6} x^{3}+\frac{5}{2} x^{2}-5 x+2, \quad x_{0}=3 \] Provide your answer below: \[ \] \( x_{2} \approx \square \)
Q:
\( \int ( 2 \pi \sin w x + 2 ^ { x } ( 2 + \frac { 3 } { 2 ^ { x } } ) - \frac { 1 } { x ^ { 2 } } - \frac { \cos e c x } { \tan x } + e x ) d x \)
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Question For the equation given below, one could use Newton's method as a way to approximate the solution. Find Newton's formula as \( x_{n+1}=F\left(x_{n}\right) \) that would enable you to do so. \[ \ln (x)+1=10 x \] Provide your answer below: \( x_{n+1}=\square \)
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17) The function \( A=A_{0} e^{-0.01155 x} \) models the amount of a particular radioactive material stored in a concrete vault, where \( x \) is a number of years since the material was put into the vault. Suppose 400 pounds of the material are initally put into the vault. Ansuer the folloving questions: a) How many pounds will be left after 130 years? (Round to nearest whole number) b) After how many yews will there be 50 pounds remaining? (Round to newest whole number)
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Approximate the area under the graph of \( f(x) \) and above the \( x \)-axis using \( n \) rectangles. \( f(x)=2 x+3 \) from \( x=0 \) to \( x=2 ; n=4 \); use right endpoints
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\begin{tabular}{l} Question \\ Use Newton's method to approximate the solution to the equation \( 7 \cos (x)=3 x+1 \). Use \( x_{0}=2 \) as your starting value \\ to find the approximation \( x_{2} \) rounded to the nearest thousandth. \\ Provide your answer below: \\ \\ \( x_{2} \approx \square \) \\ \hline\end{tabular}
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3.1.2 \( \int \frac{-3 x}{\sqrt{x^{2}-9}} d x \) 3.1.3 \( \int \frac{1}{x^{2}-4} d x \)
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Question Use Newton's method to approximate the solution to the equation \( \sqrt{x+10}=4 x^{2}+3 x \). Use \( x_{0}=2 \) as your starting value to find the approximation \( x_{2} \) rounded to the nearest thousandth. Provide your answer below: \( x_{2} \approx \square \)
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Question For the equation given below, one could use Newton's method as a way to approximate the solution. Find Newton's formula as \( x_{n+1}=F\left(x_{n}\right) \) that would enable you to do so. \[ \sin (x)=6 x-5 \] Provide your answer below: \( x_{n+1}=\square \)

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